A well-formed sudoku puzzle has a unique solution. While it is certainly possible to construct a grid for which two or more "solutions" are possible, such puzzles are generally considered to be invalid.

There are a large number of "difficulty rating" schemes in use, and as far as I'm aware, there is no widely accepted standard for rating the difficulty of a particular puzzle. These schemes are heuristic and usually count the number of "tough" logic steps needed to solve the puzzle. They may also account for the particular kind of logic necessary -- a puzzle that does not require "advanced techniques" (x-wing, xy-wing, swordfish, coloring, etc) will generally be considered to be much easier than a puzzle that requires the use of one or more of these more intricate logical processes. dcb

If the puzzle indeed has a unique solution, you can use that knowledge to help solve the puzzle. About once a week I run into this situation. There is a rectangle formed by four values, across several of the small squares. Let's say that three of the values (corners of the rectangle) are exactly the same, 2,7. The fourth one is 2,7,5. If all four are 2,7 there would be two solutions, because 2 and 7 could be interchanged for each other. The only way for that to not happen is for that fourth value to be 5. In every case that I have encountered, this has indeed been the case. It works only when three of the corners have the same two numbers, and the fourth corner has three, two of which are the same as the other corners. OF course, if it is a poorly designed puzzle, perhaps there would be two solutions. I suspect, however, that the computer generated puzzles are unique. Counting on that is helpful.

Yesterday I was doing one of the "Nightmare" puzzles, and when I was down to only four unsolved cells, they formed a rectangle with the "deadly pattern", with each corner holding a "34." I could have used one value or the other, and "solved" the puzzle, in that the result would have met the requirement of every row, column and box containing 1-9 with no duplicates. However, I know that the puzzle had one and only one solution, so I erased the whole thing and started over.